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lfunc_lfunctions • Show schema
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{'Lhash': '1098189080240903386571383479521', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.659470158300444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [7, [1, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6720.1', 'coefficient_field': '1.1.1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 1], [1, 4, 11], [1, -6, 13], [1, -6, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, 4, 43], [1, -4, 47], [1, -6, 53], [1, 12, 59], [1, -10, 61], [1, 4, 67], [1, -8, 71], [1, 14, 73], [1, -8, 79], [1, -12, 83], [1, 6, 89], [1, 14, 97], [1, 2, 101], [1, 0, 103], [1, -20, 107], [1, -2, 109], [1, 10, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 4, 11], 1]], [[[1, -6, 13], 1]], [[[1, -6, 17], 1]], [[[1, 0, 19], 1]], [[[1, 4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 0, 31], 1]], [[[1, 2, 37], 1]], [[[1, -2, 41], 1]], [[[1, 4, 43], 1]], [[[1, -4, 47], 1]], [[[1, -6, 53], 1]], [[[1, 12, 59], 1]], [[[1, -10, 61], 1]], [[[1, 4, 67], 1]], [[[1, -8, 71], 1]], [[[1, 14, 73], 1]], [[[1, -8, 79], 1]], [[[1, -12, 83], 1]], [[[1, 6, 89], 1]], [[[1, 14, 97], 1]], [[[1, 2, 101], 1]], [[[1, 0, 103], 1]], [[[1, -20, 107], 1]], [[[1, -2, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-6720-1.1-c1-0-38', 'leading_term': '2.84427330422493167358953075466000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6720/2/a/ca', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 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1.4761125166708766, 1.1906090635801674, 0.7936536244559587, 0.3171726981153924, -0.20327197684076398, -0.7308211029936793, -1.2296991468043097, -1.6674835177245197, -2.0171136005789685, -2.258509290724263, -2.379695085898743, -2.3773592259233163, -2.256815631184276, -2.031376915204505], 'positive_zeros': ['0.866318431942669414855754125470549', '1.86667740758976803700676676473328', '2.86884102246919627303174831445504', '3.41568626644521826333185054620287', '4.25430189833371268631742643280658', '5.29650177873196666869254120531200', '5.85610017830053059595425516833057', '6.51180499899169287253108952792720', '7.41714779686015809378372396533435', '8.115660799191979672036164204632573'], 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 2006039470077520729, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.866318431942669414855754125471', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.86667740758976803700676676473', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86884102246919627303174831446', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.659470158300444, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -4, 0, 6, 0, 1, 0, 6, 0, 0, 0, -1, 0, -4, 0, 1, 0, 1, 0, 6, 0, 0, 0, -4, 0, -1, 0, -2, 0, 6, 0, 2, 0, -4, 0, 1, 0, 4, 0, 1, 0, 6, 0, 6, 0, -4, 0, 0, 0, -12, 0, 10, 0, -1, 0, 6, 0, -4, 0, -4, 0, 8, 0, -14, 0, 1, 0, 4, 0, 8, 0, 1, 0, 12, 0, 6, 0, 6, 0, -6, 0, -6, 0, 0, 0, 0, 0, -14, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 14, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, 4, 11], [1, -6, 13], [1, -6, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, 4, 43], [1, -4, 47], [1, -6, 53], [1, 12, 59], [1, -10, 61], [1, 4, 67], [1, -8, 71], [1, 14, 73], [1, -8, 79], [1, -12, 83], [1, 6, 89], [1, 14, 97]], 'index': 38, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6720/ca', 'ModularForm/GL2/Q/holomorphic/6720/2/a/ca/1/1', 'ModularForm/GL2/Q/holomorphic/6720/2/a/ca'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-6720-1.1-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2006039470077520729, 'z1': {'__RealLiteral__': 0, 'data': '0.866318431942669414855754125471', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21723279
{'Lhash': '1098189080240903386571383479521', 'Lhash_array': ['1098189080240903386571383479521'], 'label': '2-6720-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/ca'}
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id: 24576372
{'Lhash': '1098189080240903386571383479521', 'Lhash_array': ['1098189080240903386571383479521'], 'label': '2-6720-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/ca/1/1'}
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id: 97168
{'Lhash': '2006039470077520729', 'Lhash_array': ['2006039470077520729'], 'label': '2-6720-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6720/ca'}